Module scores. At a university, students are graded based on their overall performance in class assessments and the scores they receive in each module in the final exam. If a student has an overall mark of 80–100, they will be awarded an “A” grade; for an overall score of 70–79, they will be awarded an “A–”; “B” for 60–69; “C” for 50–59; and “D” for 40–49. If they score below 40, they will be marked as “Fail”. Assume that the overall mark for a module follows a normal distribution with a mean of 70 and a standard deviation of 5.5.

a. Consider the students with the top 10% of marks. What is the lowest mark and grade for these students?

b. Consider the students with the lowest 30% of marks. What is the highest mark and grade for these students?